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Sunday, 17 July 2011

Induction: A peculiar little discussion in tractate Gittin 28a

In what follows, I copy the soncino translation of tractate Gittin 28a. I intersplice the text with my italicised comments. I have nothing of real interest to say about this excerpt. That's why I'm appealing for your help! If we don't want to reduce the Talmud's second response, on behalf of Raba below, to absurdity, how should we interpret it?

The exceprt talks about a person who is delivering a Get (a bill of divorce) from a husband to a wife. The divorce doesn't take effect until the Get reaches the hand of the wife (or her appointed agent). Only a living man can divorce his wife, so the rabbis discuss what justifies the messenger's assumption that the husband is still alive at the point of delivery to the wife.

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MISHNAH. IF, WHEN THE BEARER OF A GET LEFT, THE HUSBAND WAS AN OLD MAN OR SICK, HE SHOULD YET DELIVER IT TO THE WIFE ON THE PRESUMPTION THAT HE IS STILL ALIVE…

GEMARA. Raba said: [This Mishnah] speaks only of an old man who has not reached the years of 'strength' [i.e. 80 years old] and of a man who is just ill, because most invalids recover, but not if he has attained 'years of strength' [i.e. over 80] or was in a dying condition, because most persons in a dying condition die.

That is to say: according to Raba, this Mishna only applies to the under 80, and to the merely sick, rather than to the dying. If the husband were older than 80 or dying, we would have no right to assume that he was still alive, and therefore couldn’t deliver the get on his behalf.

Against this [opinion] Abaye raised the following objection [quoting a braita - a text from the generations of the Mishna]: 'If when the bearer left the husband was old, even a hundred years old, he yet gives it to the wife on the presumption that he is alive.'

The braita that Abaye quotes clearly seems to contradict Raba’s understanding of our mishna. Our mishna doesn’t just apply to the under 80, it even applies to an 100 year old. The Gemara gives Raba two options in reponse.[First response] This is a refutation [i.e. Raba concedes defeat. The law is that we assume the husband is alive however old he was when he sent the Get - or at least until he reaches 100. Second response:]. I might, however, still answer that if a man reaches such an age he is altogether exceptional [The aramayic for this second response is: ceivan de'iflig, iflig.].

The second response is the one I want us to think about for a minute.

The resolution between the mishna, according to Raba, and the braita, is supposed to run as follows: Until 80, a person who you recently left can be presumed to be alive; after 80, he cannot be presumed to be alive, because most 80 years olds don’t have all that long left; but, past a cetain age, and up until at least 100, you can once again presume that he’s alive because he has somehow defied our normal expectations with regard to longeivity. How many laws of nature do you have to defy before it would be imprudent to make any assumptions about you whatsoever?

So now, somewhere past 80, say 90, we form a new expectation: he’s not dead! But how long can we go on assuming that for?! Does the assumption stop at 100? And if we have no right to assume past 90, why start assuming again past 100? Is there some magic decade where we're protected from death? Or, given the ambiguity of the passage, is the magical period open-ended, extending 'even' to 100, but not ending there?

Can we make sense of this second response? What does it say about induction, for instance? I have nothing all that interesting to say for myself about it, but, given the principle of charity, I’d certainly like the second response to seem less absurd.

Unfortunately, the classical commentaries give this discussion very little time! And, please read my comments below, where my problem with this gemara has been made much more clear, with your help...

16 comments:

Sam - sorry if I'm being obtuse, but I'm not sure I see what seems absurd about it. Here's what I thought it meant: say, most 80 year olds (or perhaps even people above the age of 80) don't make it to 81 (in our experience), but (i) most ~90 year olds do make it to 91 (in our experience), or (ii) we don't have much data on 90 year olds, but we think they must be especially healthy or lucky or Providentially-selected if they lived that long. I understood Raba to be taking claims like these into account, not as the sole basis for his psak, but as a counterweight to the presumption, or "hazaka d'mei'ikara" that the person has.

Now, do you think it's absurd because you think the statistical claims have been shown to be false (empirically)? Or do you think there is some Sorites problem here - if so, why is that specifically for Raba and not for Abaye? Or do you think they are assuming there is some sort of miracle here? Or do you think I have misunderstood Raba's rationale? Sorry for all the questions!

Hi guys! - Yishar kochachem for setting this up. I have been meaning to write you all an e-mail for a while now to say: Thank you so much for all the e-mails - I havenlt had a chance to read any of them, but hope to be able to once I'm a little free-er. Then I was going to suggest that you post them on a blog, so that I can come back to them, all in one place, at a later date... You;ve set yp the blog - now I think you should post the recent exhcnage...

Anyway - onto Sam's post: I understood Sam's problem to mainly be regarding Aaron's second option. Namely, 80 is pretty old, and 90% of 80-year-olds will die within the year; but if you are one of tyhe lucky/healthy/blessed 10%, then we expect you to live for a good long time yet - the fact that you are of the only 10% who got this far, give sus reason to ingfer that there is something about you which will enable you to live even longer. - then I take Sam's roblem to be: this reasonong only gets stronger and stronger - but that, in turn, leads to highly counter=intuitive results. namely, the older someone is, the older we expect them to live (so, if you have got to 100, we'll expect you to go to 120, and if till 120, we'll expect you to go to 160, and if...). But surely at a certain point, the reasoning *must* flip round again, and the older the person gets, the more we must expect the,m to die all the sooner... So Sam is worried that this general form of reasoning can;t be extended, but nor can it be stopped in a principalled way anywhere befure it becomesimplausible. --- Is this right, Sam, as a diaglosis of your concern??

Well, all I'll say is: death is indeed a defier of induction. Afetr all, you might say: every further day I live, my inductive evidence that I will live yet another day, gets stronger and stronger - and so it goe so., getting stronger and stronger until - suddenly I die. It follows that by inductive canons, it is almost always irrational to think that you will ever die! --- And what abiut what I might call the 'bridge quandry'... - A: 'Iam afraid of crossing that bridge, the fall is so far!' B: 'Don't be silly, 4 millionm cars drive across this bringe every day!' A: 'Is that meant to help! - FOUR million?!! - It's *bound* to collapse soon!' (Whose reasoniong is better, A's or B's?).

Either way, you're right. My problem is with the second option that Aaron presents. You phrase the problem in terms of when and how the pattern of reason flips in on itself. That problem is certainly related to the sorities paradox. What numbers are the exact magic numbers. I'm sure that's part of my discomfort. But, as I drafted a response to Aaron last night, I put forward two other concerns, related, but more obviously divorced from vagueness concerns.

Aaron, you locate exactly what I need to do in order sufficiently to problematise this passage. But I think I can.

First I want to clarify, my main problem here isn't vagueness. Though, you're right, it's a worry for both Abaye and Raba here. Abaye's open ended presumption that a person won't die in the time it takes to deliver a get, however old they were when they sent it, becomes more and more difficult to maintain as the husband gets older and older. Yes, there's sorities issues here. But that's not the issue I'm raising. I want to concentrate on Raba's second response to Abaye.

You give a number of possible theories that we could attribute to Raba:

(1) most 80 year olds don't make it to 81 (in our experience), but most 90 year olds do make it to 91 (in our experience).

(2) we don't have much data on 90 year olds, but we think they must be especially healthy or lucky or Providentially-selected if they lived that long.

Now, the first claim makes a lot of sense. Of course, the empirical data would have to back it up, but the thesis certainly isn't absurd on the face of it. There may be such a bell curve that lasts until a certain age - perhaps even, 100. But I'm convinced, from the language that Raba uses, that (1) is the wrong understanding. 'Ceivan de'iflig iflig'' sounds much more like claim (2): since this person has set himself apart from the norm, we no longer treat him normally. This sounds more like your second possible theory, namely, claim (2).

But (2) is problematic for a number of reasons. The idea that we should suspend the principles of induction when thinking about a specific person with the claim that, 'oh they're especially lucky, or providentially selected' is at least prima facie bizarre. What does it mean to suspend the principles of induction for this person? Surely we should expect the unexpected to cease. Surely we should expect the statistical anomaly to be fleeting. This person is living on borrowed time. Every day that they live past their statistically callibrated life expectancy, we would expect to be their last.

Secondly, claim (2) seems to amount to the following: vis-a-vis person x, expect the unexpected. Induction has taught us that person x defies expectations. But that principle is unstable for the following reason: if we've come to expect the unexpected from person x, then the least expected thing for them to do would become the most expected!

Person x never does what we expect, and we except that they're going to die. But because we know that they do the unexpected, we should expect that person x will live on. But, now that we're expecting person x to live on, surely he'll do the unexpected, and die! The principle yields two conflicting outcomes: expect him to live, because that would be unexpected, and expect him to die, because we don't expect him to the expected.

In short, I want to make sense of claim (2) because linguistically, that seems to be the claim that Raba is making. But claim (2) has these two problems, at least as I understand it:(i) Surely we should expect statistical anomalies to be short-lived.(ii) 'Expect the unexpected' is an unstable prinicple.

This dicussion reminds me of a scene in the British sit-com, Blackadder, in which a soldier in WWI discusses tactics with a General:

General: We're going to leap over the trenches and walk very slowly towards the enemy.

Soldier: But isn't that what we did last time, and the time before that, and the 18 times before that?

General: Yes! And that's what so brilliant about it. The last thing that they'll be expecting is for us to do the very same thing again!

I think this first attempt at a blog is proving that the real substance lies in the discussion. Until I was forced by you guys to put my problem more clearly, I hadn't really uncovered the problem that I was merely sensing. Now that we've got a handle on what makes this Gemara peculiar, can we sort it out?

I don't think the undisputed presumption that the husband is alive (until the age of 80) is based on a principle of induction (where I suppose it would be induction over instants of time since Reuven was born?), such that Raba is calling for us to "suspend the principles of induction" (as Sam puts it). Rashi notes on the Mishna that the ruling of the Mishna is based on the principle of Chazaka D'mei'ikara. Now, this may sound like induction, but I don't think it is, for at least the following reason: induction ought to be temporally symmetric (the generalization from the observed to the unobserved goes both backward and forward in time, and if there is a conflict in observations, no "preference" is given to the earlier one), whereas Chazaka D'meikara is temporally asymmetric, or at least most opinions seem to hold this (see Tosafot in Hulin 10b, although cf. the machloket Rav and Sh'muel in Kidushin 79 I believe). Thus, if the situation was one way at t1, and then a different way at t2, and we don't know how things were between t1 and t2, then we assume it stayed the way it was at t1 all the way up until t2 (when it changed). So it seems like we are dealing with some principle that goes like this: assume that things stay/ed the same as long as is consistent with that you know. I don't think that induction could justify this, and it seems to me to be a formal/legal principle that is sui generis.

The relevance of all this for Sam's issue is this, I think (I suggested this briefly in my first comment): Rava is not claiming that we are to suspend inductive reasoning when we are dealing with an apparently exceptional case; he is saying that from the age of 80, we can no longer rely on the legal principle of Chazaka, because we have statistical (or Scriptural?) data that supports an opposite conclusion. But then once a person hits some other age, we don't have (sufficient) data one way or the other. At that point, I think Raba is saying, we fall back on the Chazaka D'meikara.

So it's not really (1) or (2), since they both suggest that Raba is arguing that once the person reaches ~90(?), we have something else to reason from - but I think Raba is saying that once the individual is so exceptional, we can fall back on the original Chazaka. Is this a far-fetched understanding of Raba?

It happens to be that I think even (2) could be justified, but I have to run...

I'm replying straight away, without giving your comment half as much consideration as it deserves.

It seems to me that your third way between (1) and (2), might well be plausible, I need to think about it some more, and check out the sources you cite. But, to me, it doesn't sound like what Raba could have meant with the words - ceivan de'iflig iflig.

His words still have the ring of claim (2) to them. So, if you could make claim (2) make sense, as you think you can, then that would be better!

That is to say: I'm with Rashi that the best reading of the mishna is the principle of chazaka d'meikara.

But I think that, by the time that Raba is trying to reconcile his understanding of the mishna with Abaye's braita, he is forced to move us into new conceptual territory with the notion of ceivan de'iflig iflig.

Of course, it would suit your general thesis about the nature of Talmudic disputes to reduce Raba's theory to a sui generis legal principle. I'm just concerned that it does a certain amount of violence to the, admitedly concise, text.

Anyway... Forgive me for another very rushed response, after an over-rushed reading of the comments accrued so far. Sam interprets Aaron's 'Option 2' in what seems to me to be a bizarre way. he says: "(2) seems to amount to the following: vis-a-vis person x, expect the unexpected. Induction has taught us that person x defies expectations. But that principle is unstable for the following reason: if we've come to expect the unexpected from person x, then the least expected thing for them to do would become the most expected!" -

I don't know if this is what Aaron meant - but is certainly not what I meant in my version of Option 2. I said, last night: "the fact that you are of the only 10% who got this far [i.e. to age 81, say], gives us reason to infer that there is something about you which will enable you to live even longer." - The principal at work here is not at all an 'induction that because this person has defied expectation, we will expect him to further defy expectations' (interesting with regard to the problem of 'counter-induction'...)!!! I will spell out what I take it to be in more detail:

90% of people die at the age of 80. This is just the way that humans are - after 80 years, their bodies wear out. However, 10% of people survive beyond 80. we ask: why is this? It's a sufficiently small group of people, that makes their survival sufficiently surprising, to warrant a search for something to explain the phenomenon. That they are 'lucky' is not so much an explanation, than it is a re-description of the state of affairs we are trying to explain. The following however (if taken in the right way) are more like explanations: the person is physically constituted different from most, to be more robust than them; or, God is keeping a special eye on him, and making sure to protect him [taking this last one in the sense that would make it a proper explanation strikes me to be taking it in a rather crude and simplistic (silly?) sense - but it certainly can be done!]. These are explanations of the anomalous and explanation-demanding phenomenon (these people's extraordinary longevity) which appeal to something further. We grant the truth of one of these things by inference to the best explanation. However, most of these explanations give us positive reason to think that the person of whom it is true will live *even* longer

Perhaps they give us reason to believe they will live until the age for which we have evidence that they start dying off - maybe it is to *this* that the chazakah demeikarah applies - and that seems to me to be quite reasonable: we know that this person has some quality (perhaps a genetic quality, perhaps someone protecting him), and this makes him live longer than usual: we don’t know *how* much longer than usual it will help hium to live, though,. we do know a rough maximum - let's say: 100. We know from experience that very few people indeed live past 100 (say, 0.5%0). So, perhaps it is reasonable to use a chazakah demeikarah, to say: he's lived beyond 80, so we'll take it to be reasonable to predict that he will live till 100, unless anything shows us otherwise. obviously this is a highly defeasible inference - but not an unreasonable one.

Consider the following: we see that most people in England die at the age of 80, apart form 10% of people. we want to explain it: so I say: well, 10% of people probably have access to better medical care than the rest, and that explains why they live longer. But this access is an ongoing thing, and will explain also why they would live on and on - pf course, until the age beyond which even good medical care cannot help you! - we know more-or-less when that is, say 100. So, we predict that people who love beyond 80, will - because of their good medical care - probably live till 100. So, this is a purely speculative prediction of a bell curve that you imagined. Of course, proper empirical investigation could completely refute its existence. But until we gather such evidence it seems quite a reasonable abductive speculation to me! (So, in conclusion: this is regular ABduction [i.e. inference to best explanation], not some strange INduction)

What do you think, Sam? It seems to me that there is not really any problem here at all...

Which leads me to my final point for now... You should post the e-mail exchange about the foundations of halacha (though I still haven't read it to be able to say what it is about in detail). And you should post it prior to this post - because I think that *that* discussion should be the kick-off for this blog, as it tries (from what I could tell by skimming) to get to the heart of understanding essential things in Jewish religion, thought, and life. This problem about induction may be interest-piquing, and may be part of 'limmud torah' in a yeshiva-ish pilpul-ish kind-of way - but it seems to me that it would be a shame if all those tools of analytic philosophy were used-up mainly on issues such as this - taking away energy and effort form the really fundamental issues and using them, instead, on the merely intriguing puzzles... Well... - that's just the opinion of an annoying anonymous comment-er... Make of it what you will!

Sam (and others), Thanks for inviting me to join. I do feel a bit out of water here but as you have been bothering me about this gemara for the better part of a year - I do feel some sort of obligation (and I am on vacation). I would like try to say something about chazaka maikara, split the difference between what I perceive as Aaron's reading of the gemara and anonymous's, say something about the machloket of abbye and rava, the language of kivan de'iflig and come back to induction. (not necessarily in that order)

1) Chazaka maikara - This would seem to mean somehting like the following - a presumption that the pre-existing state halakhic state of affairs continues on. This can be understood one of three ways a)the fact that things have been in the world a certain way at t1 indicates that they are such at t2 (some sort of clarification of matter of fact\birur or more aptly "strong birur" b)the fact that things have been in the world a certain way justifies us in positing\projecting that state into the future\projection or "weak birur" (for the lamdanim reading this)c)status quo - i.e. a status of persons or objects exists and until evident to the contrary the status stands as such - I would call this non-chronological status quo\convention - in our case the person has a status of living (until proven otherwise). I believe that Aaron intended his claim of "chazaka maikara" as a sui generis principle unrelated to induction to indicate that chazaka maikara should be understood in the third way (c)

2) I take it as obvious that rava cannot hold (c), at least according to the statement of admission attributed to him in the gemara. While "majority of gossim lemita" is a piece of evidence that can overturn (c) - I find it hard to believe that "gevurot" - above 80 is parallel. It is not sufficient to overturn (c). Hence Rava holds (a)clarification of matter of fact\strong birur or (b)projection\weak birur.To put this in more lamdani terminology - above 80 is at most a "raiuta" (undermining) of the chazaka - only (a) or (b) are susceptible to reiuta - not (c). Hence if rava accepts reiuta (as oppossed to abbaye) he holds either (a) or (b). 3) Argument of abbaye and rava. I take it that (a) is patently absurd. There is no way that the past can be indicative in a strong way of the future. I do not believe that we need to be formal Humeans to make this claim. I think it can be proved from many sugyot both in Halakha and Machshevet Chazal. So the argument of Abbaye and Rava comes down to Rava holds (b\projection - hence reiuta - above 80 undermines\prevents\blocks\makes us wary of our projection. Abbaye holds (c)non-chronological status - hence even if the person is 100 absent evidence to the contrary he has a status of living. 4)The second answer - kivan de'iflig - if I am correct Ravs is animated by the sensibility that projections regarding the future are legitimate but sometimes unwarranted\absurd. In the case of 100 years old we have two competing projections which are both unwarranted\absurd. Projection 1 - a person above 80 is still alive. Projection 2 - the person above 80 will probably die sometime quite soon. The statement of "kivan d'iflig etc" in the gemara presents the problematic of projection 2 against the problematic of projection 1 (raiuta of the raiuta). As such we are left with "no projection". Aaron (I believe) said this means we return to "chazaka maikara". I don't think this is correct. For Rava that would mean projection 1 - which is patently absurd. Anonymous says that kivan d'iflig means that projection one is reasonable - I disagree. I would like to suggest that in the second answer of the gemara - rava faces a situation of agnosticism regarding projections - we are left with a situation of a woman with a get in her hand - with no knowledge\projection regarding the husband. Hence she is megureshet. We are willing to give up claims regarding that which is not in front of us (another crucial halakhic principle).

5)kivan d'iflig, induction and agnosticsm- I would like to suggest that Sam's original intuitions regarding induction our sugya are somewhat correct. If I remember correctly "the problem of induction" involves assuming constancy from t1 to t2. As indicated earlier I think Chazal would agree with this. But this does not mean that Chazal would object to 1)quasi-formal positing of constancy from t1 to t2 (rava above) or 2) the existence of formal legal status of persons and objects (abaye above). At the same time, a case of "reiuta" might rehabilitate the proto-Humean intutitions I claim already exist in Chazal - at some point quasi-formal positing becomes impossible\absurd. In yet another case - a counterintuition\example might make the inherent posit of the reiuta seem impossible\absurd - an absolute exception to the rules of the game i.e. kivan de'iflig - the result is a kind of agnosticsm\lack of positing. In the case of Gittin 28a - megureshet (but we could imagine an acharon claiming safek megureshet \megureshet lechumra for the gemara's second answer.